Oh wow, I don't know what to say about those. There's many of them, and all happened recently which means in theory there should be many more.
I know double-spending is not actually possible with Bitcoin, but this may be beyond my level of understanding. DannyHamilton, could you please break this down and explain to me and the beginners that are present? I feel like I'm probably just misunderstanding something here.
Understanding what you are seeing at that link requires a pretty good technical knowledge about exactly how bitcoin transactions work. These are technical situations involving transaction inputs and outputs.
As a simple example though...
If you create a transaction that sends a very small amount of bitcoins (for example 0.00001 BTC) and you don't include a transaction fee with your transaction...
Or if you create a very large (in bytes, not in bitcoins) transaction (such as 5000 bytes) and you don't include a transaction fee with your transaction...
You might discover after several days that no miners have bothered to confirm your transaction yet. Therefore, your transaction is still "unconfirmed" several days after you sent it.
Transactions that do not get confirmed take up space in the memory pool of peers. Those peers want to use that space in their memory pool for transactions that actually have a chance of getting confirmed eventually. Therefore, peers will start dropping unconfirmed transactions that are a few days old from their memory pool. Eventually most of the network forgets that the transaction ever existed, and the bitcoins are once again available for you to send from your wallet (since they never actually got where they were going). Some wallets will simply re-transmit the original transaction repeatedly forever waiting for it to confirm. However, some wallets (such as blockchain.info/wallet) will return the bitcoins to your balance and allow you to create a new transaction with the bitcoins.
If you create a new transaction (perhaps sending the exact same amount to the exact same person as before, only this time with a transaction fee), then blockchain.info will see that a new (different) transaction is re-using the same bitcoins that they saw in the earlier transaction that never confirmed. Blockchain.into will label this as a "double spend" since it saw the same bitcoins in two slightly different transactions, and they will add it to that linked web page.
There are more complex situations where this can occur, and it relies on exactly which outputs are being spent in the transactions, but as a user level explanation that's a pretty good example.